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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:A local analog of the Grothendieck conjecture for
higher local fields - Abrashkin\, V (Durham)
DTSTART;TZID=Europe/London:20090825T093000
DTEND;TZID=Europe/London:20090825T103000
UID:TALK19585AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/19585
DESCRIPTION:Suppose K is an N-dimensional local field where N
is a non-negative integer. By definition\, if N=0
then K is just a finite field\, otherwise\, K is a
complete discrete valuation field and its residue
field is an (N-1)-dimensional local field. Let G
be the absolute Galois group of K. If N=1 then the
structure of the topological group G depends only
on very weak invariants of K and is not sufficien
t to recover uniquely the field K. The situation b
ecomes totally different if we take into account t
he filtration of G by its ramification subgroups.
Then the corresponding functor from the category o
f 1-dimensional local fields to the category of pr
ofinite groups with decreasing filtration is fully
faithful. In the talk it will be discussed an ana
log of this statement for higher local fields and
its relation to the Grothendieck conjecture in the
context of global fields.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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